He had already pushed back shows in Anaheim, Calif., and Vancouver because of "production logistics," and this week had to postpone his Chicago dates because of damaged equipment.
Upcoming locations include Denver and Minneapolis, which may be affected as well.
He may have to push back several more performances, as the truck contained the rapper's 60-foot LED screen and other critical pieces of equipment.
"The gear is central to the staging of The Yeezus Tour, and central to the creative vision put forth by Kanye West and his design team at Donda," a rep said.
"As a result of this event," the representative added, "it is impossible to put on the show and the Yeezus Tour will be postponed until these essential pieces can be reengineered and refabricated."